Much of the performance analysis on multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems is focused on worst case near-far scenarios. The user capacity of power-controlled networks with multiuser receivers are less well-understood. In 1, it was shown that under some conditions, the user capacity of an uplink power-controlled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. In the present paper, we show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signal-to-interference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirements. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.